At the beginning of this year, we discussed why buying puts against existing shares (protective put strategy) was not optimal. With the market witnessing large downside in recent times, the urge to buy a stock at lower levels and then a put to protect losses on the stock seems to be greater. In this article, we discuss how a long call is comparable to a protective put and why buying a call is better.
Call or Protective Put
Suppose you buy a put option against a long position on an underlying; if the underlying moves up, the put will expire worthless, but the underlying will generate gains. On the other hand, if the underlying declines, the stock will suffer losses, but the puts will generate gains. If the intrinsic value of the put offsets the loss in the underlying, your total loss will be limited to the cost of the put.
For instance, you pay 25 points to buy a near-month 500 put on a stock that is trading at 500. If the stock trades at 400 at option expiry, the 500 put will be worth 100 points, which is the intrinsic value of the option. Note that the time value of an option will be zero at expiry. The stock would have lost 100 points. Therefore, the total loss on the position is limited to 25 points — the cost of the put.
Traders often simultaneously buy a stock and a put option. The characteristic of this position is the same as buying a put against an existing stock position. Technically, however, the former is called as married put and the latter, as protective put.
Now, instead of setting up a protective put or a married put, what if you buy a call option on the underlying? The characteristic of this position is similar. How? If the underlying moves up, you generate profits on the call. Suppose you buy the 500 call for 30 points. If the underlying moves up to 600 at expiry, your call gains 70 points (100 points of intrinsic value less 30 points cost). In the case of the protective put, the gains would be 75 points (100 points on the stock less 25 points cost). If the underlying declines, the loss is limited to the cost of the call. In case of a protective put, the loss would be limited to the cost of the put. Note that your gains will be higher or your losses lower if you were to close the position before expiry because you can capture some time value when you sell the call.
If long calls are comparable to protective puts, what does this mean for your trading strategy? You might as well set up a long call for two reasons. One, it requires lower capital outlay compared to protective put. And two, long call is operationally efficient to set up, as a protective put has two legs — a long stock and a long put.
The delta of an underlying is one, as it is the change in the underlying with respect to itself. From the Black-Scholes-Merton (BSM) model, we know that the delta of a call option is N(d1). As puts move in the opposite direction to the underlying, the delta of a put is N(d1)-1. That is, puts have negative delta. So, a protective put will have a delta of N(d1)- delta of 1 for the underlying plus N(d1)-1 for the put. Therefore, the net delta of a protective put is equal to the call delta.
Note that delta is valid for only small price changes in the underlying. The objective was to show that a long call is comparable to a protective put by looking at each position’s delta. The intention is not to dynamically replicate a protective put with a long call.
(The author offers training programmes for individuals to manage their personal investments)